Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -32}$ ${x+5y = 44}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${-2x-2y = -32}$ $2x+10y = 88$ Add the top and bottom equations together. $8y = 56$ $\dfrac{8y}{{8}} = \dfrac{56}{{8}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-2x-2y = -32}\thinspace$ to find $x$ ${-2x - 2}{(7)}{= -32}$ $-2x-14 = -32$ $-2x-14{+14} = -32{+14}$ $-2x = -18$ $\dfrac{-2x}{{-2}} = \dfrac{-18}{{-2}}$ ${x = 9}$ You can also plug ${y = 7}$ into $\thinspace {x+5y = 44}\thinspace$ and get the same answer for $x$ : ${x + 5}{(7)}{= 44}$ ${x = 9}$